Question

The current price of Kinston Corporation stock is $10. In each of the next two years, this stock price can either go up by $3.00 or go down by $2.00. Kinston stock pays no dividends. The one year risk-free interest rate is 5% and will remain constant.

Using the binomial pricing model, calculate the price of a two-year call option on Kinston stock with a strike price of $9.

Answer 1

It is a two year binomial model. We will first calculate value of call option at year 1 for up and down branches of year 2. Then we would finally solve for the value of option at year 0.

YEAR !

UP branch

Value of call in the up state at period one using binomial model is given by

C=SD+B, where D=(Cu-Cd)/(Su-Sd)

Cu, Cd are the call payoffs during up and down moves respectively. Su and Sd are stock price during up and down moves respectively.

and B = (Cd-Sd*D)/(1+Rf) and S is the stock price for that period. Here at up node at year 1 it is 13. Rf is risk free rate = 5%

D = (7-2)/(16-11) = 1

B = (2-11*1)/(1.05) = -8.57142

Therefore, as per formula, C = 13*1+(-8.5714) = $4.43

Down Branch

D=(2-0)/(11-6) = 0.4

B=(0-6*0.4)/(1.05) = -2.2857

Thus, Value of call in the down state at period one using binomial model is given by, C=SD+B

S here is 8.

C=8*0.4+(-2.2857) = $0.91

YEAR 0

Now we find value of call using up and down states call value at year 0

D = (4.43-0.91)/(13-8) = 0.704 (The values of Cu and Cd are used as calculated above)

B = (0.91-8*0.704)/1.05 = -4.497

Thus, C= 10*0.704-4.497 = $2.54

Thus, the price of a two year call option on Kinston stock with strike price of $9 is $2.54